max_input_vars is to 40 000 (sic!). Default was 1000 than we changed to 2000, next 4000 and finally 40 000. No changes at all

Thank you so much for the great community suport. We had to buy a full hosting for the survey from LimeSurvey, so the problem is not urgent now. We will try to solve it for potential future adoption.

With 10000 it can't be max_input_vars, something other .

Do you have access to the server log ? If yes : do the action with tail the webserver error log.
Then you have the information , then the way to fix it.